System and method for forecasting floods

ABSTRACT

A method for forecasting flood, the method including: calibrating the hydrological model by using an objective function that is a sum of squared difference between the observed streamflow and the corresponding forecasted streamflow at each lead time to obtain the optimized hydrological model; using the optimized hydrological model to forecast floods; and evaluating forecasting performance of the optimized hydrological model. The method improves the forecasting accuracy and provides forecasting results at various lead times.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of and claims domesticpriority to U.S. patent application Ser. No. 15/377,974, filed Dec. 13,2016, now pending, which under 35 U.S.C. § 119 and the Paris ConventionTreaty claims foreign priority benefit to Chinese Patent Application No.201510932746.0 filed Dec. 15, 2015. The contents of all of theaforementioned applications, including any intervening amendmentsthereto, are incorporated herein by reference. Inquiries from the publicto applicants or assignees concerning this document or the relatedapplications should be directed to: Matthias Scholl P C., Attn.: Dr.Matthias Scholl Esq., 245 First Street, 18th Floor, Cambridge, Mass.02142.

BACKGROUND OF THE INVENTION Field of the Invention

The invention relates to a system and method for forecasting floods atmultiple lead times.

Description of the Related Art

A conventional method for flood forecasting is as follows: 1) collectinghistorical hydrological data with gauges for a basin, 2) establishing ahydrological model, 3) implementing parameters calibration with respectto the hydrological model with a determined objective function, 4)sending the forecasts to the manager computing devices, and 5)evaluating the performance of the hydrological model using forecastingevaluation criteria.

In general, a conventional method uses real-time observed or weatherpredicted rain fall data. The lead time of forecast is relatively shortdue to the poor timeliness of the observed rainfall collected fromgauges, or the forecasting accuracy is relatively low due to theuncertainty of weather-predicted rainfall.

In addition, the conventional methods are aimed at hydrologicalsimulation rather than forecasting; thus, the objective functions arebuilt to reflect the rain-runoff relationship, which have littleforecasting ability.

In addition, evaluation criteria in the conventional methods only focuson forecasted result at a single lead time and is unable tosimultaneously describe the forecasted results at multiple lead times.

SUMMARY OF THE INVENTION

In view of the above-described problems, it is one objective of theinvention to provide a method and a system for forecasting floods atmultiple lead times.

To achieve the above objective, in accordance with one embodiment of theinvention, there is provided a method for forecasting flood at multiplelead times. The method comprises:

-   -   1) obtaining hydrological variables comprising precipitation and        evaporation for a basin, in which the precipitation is obtained        by measuring rainfall data with radars, rain gauges, and        precipitation micro-physical characteristics sensors (PMCSs) and        by combining the rainfall data from the radars, the rain gauges,        and the PMCSs;    -   2) collecting historical flood information for the basin to        estimate a mean concentration time of the basin and to determine        a maximum lead time k;    -   3) obtaining a series of observed streamflow Q_(t) ^(obs) from a        hydrologic station at the outlet of the basin, in which the        observed streamflow Q_(t) ^(obs) represents the observed        streamflow at a time t; t is an integer, and 1≤t≤N; and N is a        total number of observations;    -   4) establishing a hydrological model, and using the hydrological        model for prediction by inputting the hydrological variables to        the hydrological model to obtain a series of forecasted        streamflow Q_(t,t-j) ^(pre); in which the forecasted streamflow        Q_(t,t-j) ^(pre) represents the forecasted streamflow at the        time t at a lead time j; j is an integer, and 1≤j≤k; and the        precipitation within lead times are neglected for the        prediction;    -   5) calibrating parameters of the hydrological model with an        objective function as follows to obtain the optimized        hydrological model:

${{\min \; F} = {\sum\limits_{t - 1}^{N}\; \left( {\left( {Q_{t}^{obs} - Q_{t,{t - 1}}^{pre}} \right)^{2} + \left( {Q_{t}^{obs} - Q_{t,{t - 2}}^{pre}} \right)^{2} + \ldots + \left( {Q_{t}^{obs} - Q_{t,{t - k}}^{pre}} \right)^{2}} \right)}};$

-   -   6) using the optimized hydrological model for prediction to        obtain results for flood forecasts at multiple lead times, and        sending the results for flood forecasts at the multiple lead        times to a manager computing device for flood prevention; and    -   7) evaluating the forecasting performance of the optimized        hydrological model by using a criterion selected from: a        Nash-Sutcliffe efficiency, a root mean square error, a water        balance index, a qualified rate of peak flow, and a qualified        rate of a peak time.

Advantages of the method for forecasting flood in the invention aresummarized as follows:

-   -   1. The predicted rainfall results obtained by using the method        of the invention are more reliable than that obtained by using        conventional methods.    -   2. The objective function for calibrating the hydrological        model, is a sum of squared difference between the observed        streamflow at each time and the forecasted stream flow at the        corresponding time at every lead time that is not longer than        the maximum lead time. The objective function allows for joint        optimization of the forecasting capabilities of the hydrological        model at multiple lead times to achieve an optimized        hydrological model.    -   3. The optimized hydrological model obtained from the method of        the invention has enhanced forecasting accuracy. In addition,        the optimized hydrological model provides forecasted results at        multiple lead times, and thus allows for providing early warning        of flood events and improving flood prevention.    -   4. The method of the invention allows for lengthening the        maximum lead time for flood forecasting.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of the method for forecasting flood at multiplelead times according to one embodiment of the invention;

FIG. 2 is a schematic diagram of comparison between the observedresults, the forecasting results of the invented method at 1-day leadtime, and the forecasting results of the conventional method at 1-daylead time;

FIG. 3 is a schematic diagram of comparison between the observedresults, the forecasting results of the invented method at 2-day leadtime, and the forecasting results of the conventional method at 2-daylead time; and

FIG. 4 is a schematic diagram of comparison between the observedresults, the forecasting results of the invented method at 3-day leadtime, and the forecasting results of the conventional method at 3-daylead time.

DETAILED DESCRIPTION OF THE EMBODIMENTS

For further illustrating the invention, examples detailing the methodand system for flood forecasting are further set forth below. It shouldbe noted that the following examples are intended to describe and not tolimit the invention.

As shown in FIG. 1, the method for forecasting flood at multiple leadtimes is as follows:

obtaining hydrological variables comprising precipitation andevaporation for a basin, in which rainfall data is measured with radar,rain gauges, and the precipitation micro-physical characteristics sensor(PMCS), and the rainfall data from the three sources are combined tocalculate the precipitation;

collecting historical flood information to estimate the average time ofconcentration for the basin so as to determine the length of lead time(i.e., the maximum lead time k for flood forecasting);

establishing a proposed hydrological model and using the proposedhydrological model for prediction to obtain the forecasted streamflow byinputting the hydrological variables (i.e. precipitation andevaporation) to the hydrological model;

calibrating the hydrological model to obtain the optimized parametersfor the model so as to result in the optimized hydrological model byusing the following objective function, which is sum of the squareddifference between the observed streamflow at each time and theforecasted streamflow at the corresponding time at every lead timewithin the maximum lead time k;

$\begin{matrix}{{{\min \; F} = {\sum\limits_{t - 1}^{N}\; \left( {\left( {Q_{t}^{obs} - Q_{t,{t - 1}}^{pre}} \right)^{2} + \left( {Q_{t}^{obs} - Q_{t,{t - 2}}^{pre}} \right)^{2} + \ldots + \left( {Q_{t}^{obs} - Q_{t,{t - k}}^{pre}} \right)^{2}} \right)}};} & (1)\end{matrix}$

in the model calibration,

^(obs) is the observed streamflow at time t (t=1, 2, . . . , N), Nis thetotal number of the observed streamflow; Q_(t,t-j) ^(pre) is theforecasted streamflow at time t at a lead time j, which is based on theinputs for forecasting at time j ahead of time t;

using the optimized hydrological model to obtain forecasted results andsending the forecasted results to devices of managers for floodprevention; and

validating the optimized hydrological model to evaluate the forecastingperformance of the model by using a widely used criterion selected from:the Nash-Sutcliffe efficiency (NSE), Root Mean Square Error (RMSE),Water balance index (WBI), the qualified rate of peak flow (QRF) and thequalified rate of peak time (QRT).

In the method, the parameters of the model are calibrated not only byusing a single optimized algorithm but also by various combinedalgorithms. For example, the estimated parameters of Genetic algorithmcan be treated as the initial values of the Rosen Brock methods, as wellas the estimates of Rosen Brock methods can treated as the initialvalues of Simplex method.

The formulas for the model validation are as follows:

$\begin{matrix}{{{NSE} = {1 - \frac{\sum\limits_{t = 1}^{N}\; \left( {Q_{t}^{pre} - Q_{t}^{obs}} \right)^{2}}{\sum\limits_{t = 1}^{N}\left( {Q_{t}^{obs} - \overset{\_}{Q_{obs}}} \right)^{2}}}};} & (2) \\{{{RMSE} = \sqrt{\frac{\sum\limits_{t = 1}^{N}\left( {Q_{t}^{pre} - Q_{t}^{obs}} \right)^{2}}{N}}};} & (3) \\{{{QRF} = \frac{NF}{M}};} & (4) \\{{{QRT} = \frac{NT}{M}};} & (5)\end{matrix}$

in which,

^(pre) is the predicted streamflow at time t;

is the mean value of the observed streamflow; W_(pre) and W_(obs) arethe total volume of the predicted and observed flow, respectively; NF isthe number of the qualified flood events about peak flow; NT is thenumber of the qualified flood events about peak time; M is the totalflood events.

EXAMPLE

The method of the invention is implemented with respect to Xunhe riverbasin which is located at the Shanxi province. The basin has a drainagearea of 6448 km2, a length of the river of approximately 218 km, and theaverage annual flow of about 73 m³/s. The basin has a subtropicalmonsoon climate which is wet and moderate with an annual averagetemperature of 15-17° C. The rainfall across the basin in summer isabundant, which accounts for a large proportion (70%-80%) of the yearlyrainfall.

In the method, 28 rainfall stations and 3 hydrologic gauged stations arespreading over the basin for data collection. The areal precipitation iscollected by applying the Thiessen polygon method to the gauge data ofthe rainfall stations, and the areal pan evaporation is computed byusing the average value of the data from gauged stations. Discharge ismeasured at the outlet of the basin. Across the period 1991-2001, dataof 1991 is used for warm-up. Data during 1992-1996 and 1997-2001 areserved for calibration and validation, respectively.

The invented method and the conventional method are both used for theflood forecasting at lead times of 1-3 days. The NSE, RIVISE and WBI areused as the evaluation indicators for model validation.

TABLE 1 Evaluation of flood forecasting performance of the conventionaland invented methods Lead Calibration period Validation period time(day) NSE WBI RMSE NSE WBI RMSE Invented 1 0.90 1.14 61.24 0.79 1.1762.36 method 2 0.62 0.90 119.09 0.57 0.94 90.16 3 0.33 0.70 157.82 0.240.75 120.42 Conventional 1 0.94 0.96 46.36 0.88 0.94 47.66 method 2 0.510.69 135.50 0.43 0.71 103.71 3 0.23 0.56 169.49 0.14 0.60 127.39

The performances of conventional and invented methods are summarized inTable 1 as above. As shown in Table 1, the forecasting accuracy of bothmethods decreases with the increased lead time. In both the calibrationperiod and the validation period, the NSE in the invented method issmaller than that in the conventional method for 1-day lead time, butthe NSE in the invented method is larger than that in the conventionalsystem for both 2-day and 3-day lead times. Similarly, the inventedmethod has significant improvements in terms of WBI and RIVISE ascompared to the conventional method for the 2-day and 3-day lead times.

FIGS. 2-4 demonstrate the comparison between the observed streamflow,the forecasting streamflow of the invented method, the forecastingstreamflow of the conventional method from 1992/1/12 to 1994/3/22. FIGS.2-4 show that the forecasting performance of the invented method isbetter than that of the conventional method for 2-day and 3-day leadtimes, especially in terms of the simulation of peak flows. In addition,FIGS. 2-4 show that compared with the conventional method, theperformance of the invented method decreases slower as the lead timeincreases, especially in terms of the simulation of peak flows.

Unless otherwise indicated, the numerical ranges involved in theinvention include the end values. While particular embodiments of theinvention have been shown and described, it will be obvious to thoseskilled in the art that changes and modifications may be made withoutdeparting from the invention in its broader aspects, and therefore, theaim in the appended claims is to cover all such changes andmodifications as fall within the true spirit and scope of the invention.

1. A method for forecasting flood, the method comprising: 1) obtaininghydrological variables comprising precipitation and evaporation for abasin, wherein the precipitation is obtained by measuring rainfall datawith radars, rain gauges, and precipitation micro-physicalcharacteristics sensors (PMCSs) and by combining the rainfall data fromthe radars, the rain gauges, and the PMCSs; 2) collecting historicalflood information for the basin to estimate a mean concentration time ofthe basin and to determine a maximum lead time k; 3) obtaining a seriesof observed streamflow Q_(t) ^(obs) from a hydrologic station at theoutlet of the basin, wherein the observed streamflow Q_(t) ^(obs)represents the observed streamflow at a time t; t is an integer, and1≤t≤N; and N is a total number of the observed streamflow; 4)establishing a hydrological model, and using the hydrological model forprediction by inputting the hydrological variables to the hydrologicalmodel to obtain a series of forecasted streamflow Q_(t,t-j) ^(pre);wherein the forecasted streamflow Q_(t,t-j) ^(pre) represents theforecasted streamflow at the time t at a lead time j; j is an integer,and 1≤j≤k; and the precipitation within lead times are neglected for theprediction; 5) calibrating parameters of the hydrological model with anobjective function as follows to obtain the optimized hydrologicalmodel:${{\min \; F} = {\sum\limits_{t - 1}^{N}\; \left( {\left( {Q_{t}^{obs} - Q_{t,{t - 1}}^{pre}} \right)^{2} + \left( {Q_{t}^{obs} - Q_{t,{t - 2}}^{pre}} \right)^{2} + \ldots + \left( {Q_{t}^{obs} - Q_{t,{t - k}}^{pre}} \right)^{2}} \right)}};$6) using the optimized hydrological model for prediction to obtainresults for flood forecasts at multiple lead times, and sending theresults for flood forecasts at the multiple lead times to managercomputing devices for flood prevention; and 7) evaluating theforecasting performance of the optimized hydrological model by using acriterion selected from: a Nash-Sutcliffe efficiency, a root mean squareerror, a water balance index, a qualified rate of peak flow, and aqualified rate of a peak time.